Mathematical Astronomy Morsels [1] 0943396514, 9780943396514

Table of contents :
The Moon
1 The instantaneous lunar orbit . . . . . . . . . . . . . .
. . 11
2 The extreme values of the distance of the Moon to the Earth 14
3 The distribution of the Moon's perigee and apogee distances 17
4 What is the mean value of the Earth - Moon distance? 21
5 Extreme declinations of the Moon .
26
6 The librations of the Moon . . .
29
7 Months with five lunar phases
37




















Eclipses and Occultations
8 The number of eclipses in a year . . . . . .
43
9 Solar eclipses : some periodicities . . . . . .
49
IO Curious and interesting facts about solar eclipses.
56
1 Regions of visibility of solar eclipses . . . . . .
62
12 When is the northem limit the southem one? . . 83
13 The frequency of total and annular solar eclipses fora given piace 88
14 Total and annular solar eclipses in dose succession at a given piace 93
15 Nearly-zenithal centrai solar eclipses . . . . . . . . .
. 98





































16 Curious and interesting facts about lunar eclipses
7 Total penumbral lunar eclipses . . . . . . . . . .
18 The half-saros . . . . . . . . . . . .
9 Series of occultations





































100
108
110
113















































3




4 MATHEMATICAL ASTRONOMY MORSELS
20 Occultations of bright stars by the Moon . . . . 124
21 Series of occultations of Satum . . . . . . . . . . . . . . . 134
22 Occultations of bright stars by the eclipsed Moon 139
23 Occultations of planets by the eclipsed Moon . . . . . . . . . 149
24 Occultations of planets by the eclipsed Sun . . 154
25 Occultations of bright stars by planets . . . . . . . .
159





















Planetary Motions
26 The barycenter of the solar system . . .
27 On the passages of Earth in perihelion
28 Periheloids and apheloids . . . . . . . .
29 A periodicity of 179 years? . . . . . . .
30 Planetary quadrants and planetary sectors ..
31 How often are the planets aligned ? . . .
32 On 'remarkable' relations between the mean motions of the planets
33 Ceres and Pallas, and other couples . . . . . . . . ..
34 Seneca, Orthos, and Quetzalcoatl . . . . . . . . .
35 Defining asteroids of the Apollo and Amor types
36 The periodic comet Encke and Jupiter ...... .
37 The orbitai inclinations of the four Galilean satellites























165
169
172
179
182
186
191
194
200
207
209
215


















































Planetary Phenomena
38 Planetary motions: approximate periodicities
39 Opposition loops . . . . . .
40 Opposition places ..
41 Triple conjunctions
42 Planetary groupings .
43 Periodicities in the phenomena of the satellites of Jupiter ..
44 Jupiter and triple shadow phenomena ..... .
45 Jupiter without satellites . . . . . . . . . . . . . . . . .
.




















































223
233
240
246
262
269
279
281



TABLE OF CONTENTS 5







On the Celestial Sphere

6 Heliacal risings and settings . . . . . . . .
7 The positions of Uranus, Neptune, Pluto and Ceres at their discovery dates . . .
. . . . . . . . . .
8 Ecliptic and galactic equator . . . . . . . . . . . . .
9 The equinoctial and solstitial points and the constellations .
50 The declination of Polaris . . . .
51 Alpha is not always the brightest










289

296
301
303
305
308




























Statistics, etc.

52 The mean frequency, yes, but ...
53 Statistics : danger !
54 Sunspots and the weather
55 Solar activity and the brightness of lunar eclipses






























313
315
319
328












































Varia















































56 The equation of time . . . ....
57 About the equinoxes and the solstices
58 The weekday of Christmas Day ...
59 The distribution of Easter Sundays
60 The date of Easter - some interesting data
61 Rounding numbers . . . . . . . . .
62 Predicting sunspot activity . . . . . . .















































337
346
352
354
361
366
370


































































Index . . . . . .. . . . . . . . .. . . . . . .
. . . . . . . . . 375

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